I'll add myself to this list here. I started my own thread but then found this one and I've read all of it. My 10.5 pro started having this issue about a month ago and I've tried everything (except hitting it). First I updated to the latest ios, and then when that didn't work I updated to the latest public beta. No luck, both times it worked for a day or 2 and then started acting up again.
I then called apple and the CS told me to try wiping it and restoring it, so I spent an hour or so doing that. Again, worked for a bit and started acting up again. I now have an appt with the apple store for saturday.
As others have said, my issue occurs randomly and seemingly without reason. The only consistent problem is that it happens more often and more severely when plugged in and charging. Turning off multi-touch seemed to work for me, still happens but not as often or as severe. I also turned on the accessibility setting as suggested earlier. Since it's such a random issue I'm worried that the apple store is going to say there's nothing wrong and send me home.
Curious, how reliable is the Touchscreen test app (Vishal Singh)? It has 4.5 stars and seems to be well regarded. Whenever I use that app it's clear that there's an issue with the screen and I'm wondering if that alone will be enough for the genius to realize there's a problem.